...people would stop saying the evidence indicates we're alone in the universe.
It quite simply doesn't.
Absence of evidence is not evidence of absence. Our exoplanet hunting techniques are only now starting to see planets small enough to support our kind of life. They are biased towards large planets and ones that are too close to their primary to be habitable.
Our chances of picking up radio signals from another star are slim. SETI is based off of assumptions and one of them is that a signal will be produced that's strong enough. Based off of our own technology, most of our radio signals are not strong enough to be heard over the noise made by the Earth, the Sun, Jupiter, etc. There's evidence that radio is not actually the best way to communicate with a spaceship - light may be better, and a laser communication would, again, likely be drowned out by the local primary.
It's possible that the answer to Fermi's Paradox is "It's just dang hard to find each other in all of this space."
Now, it's intriguing to explore the idea that we may actually be one of the first intelligent civilizations to arise, and there's some evidence that supports it.
But we need to stop saying we're alone. We just don't have enough evidence to say that yet.